In order to stay close to schemes which are feasible with current technology,
we also analyze the effect of the mixedness in the probe states. In this case,
we study the channel discrimination by fixing not only the total energy of the
input state but also its total amount of squeezing. Then, we are able to show
that two-mode squeezed thermal states are always better than their single-mode
counterpart when all the thermal photons are directed into the dissipative
channel. We have numerically verified that this result also holds,
approximately, for unbalanced distribution of the thermal photons. Finally, we
also investigate the role of correlations in the improvement of loss
detection. In order to quantify correlations, besides entanglement and mutual
information, we exploit the recent results on the quantum
discord [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, which has been
defined with the aim of capturing quantum correlations in mixed separable
states that are not quantified by entanglement. Thus, at fixed input
squeezing, we study the reduction of the QCB as a function of various
correlation quantifiers, i.e., quantum mutual information, entanglement and
quantum discord. This analysis allows us to conclude that employing squeezing
in the form of correlations, either quantum or classical, is beneficial for
the task of loss detection whenever squeezed thermal states are considered as
input probes.
